Modeling dynamic behavior of two magnetic microbubbles in ultrasonic and magnetic fields

Magnetic microbubble (microbubble coated with magnetic nanoparticles) has the advantages of hybrid encapsulated shell, non-invasive fields manipulation and drug/gene delivery, which promotes a broad application prospects in both scientific research and clinic communities. In this work, the encapsulated shell coated with magnetic nanoparticles has been translated into the equivalent problem about bubble in the magnetic fluid. Behavior of two bubbles in the magnetic fluid are theoretically studied by using Lagrange formalism. We evaluate the manipulation of acoustic and magnetic fields on two bubbles dynamics. Magnetic pressure generated by magnetic field increases the pulsating amplitude of each bubble, affects bubbles translation and enhances the gas pressure and temperature inside bubble. Besides, bubbles attraction is caused by the competition between viscous drag and attractive secondary Bjerknes force related to bubble pulsation. In addition, the attractive force caused by magnetic field is useful at very close distance between bubbles, and its effect is quite small compared to the attraction driven by ultrasound. These findings may have implications for ultrasound guided drug delivery using microbubbles coated with magnetic nanoparticles, especial their manipulation in magnetic field.